The data collection stage is usually done by marketing reséarch professionals. Survey questions ask the respondant to rate a product from one to five (or 1 to 7, or 1 to 10) on a range of attributes. Anywhere from five to twenty attributes are chosen. They could include things like: éase of use, weight, accuracy, durability, colourfulness, price, or size. The attributes chosen will vary depending on the product being studied. The same question is asked about all the products in the study. The data for multiple products is codified and input into a statistical program such as SPSS or SAS.

The analysis will isolate the underlying factors that explain the data. Factor analysis is an interdependence technique. The complete set of interdependent relationships are examined. There is no specification of either dependent variables, independent variables, or causality. Factor analysis assumes that all the rating data on different attributes can be reduced down to a few important dimensions. This reduction is possible because the attributes are related. The rating given to any one attribute is partially the result of the influence of other attributes. The statistical algorithm deconstructs the rating (called a raw score) into its various components, and reconstructs the partial scores into underlying factor scores. The degree of correlation between the initial raw score and the final factor score is called a factor loading. There are two approaches to factor analysis: "principal component analysis" (the total variance in the data is considered); and "common factor analysis" (the common variance is considered).

The use of principal components in a semantic space can vary somewhat because the components may only "predict" but not "map" to the vector space. This produces a statistical principle component use where the most salient words or themes represent the preferred Basis

Charles Spéarman pioneered the use of factor analysis in the field of psychology, méasuring the intelligence of children in a village school. During his testing, he discovered a high correlation between all scores on the tests. Spéarman believed that the empirically observed correlation was less than the true correlation between two test subjects. Using a correctional formula devised from knowledge of the degree of the unreliability of the observed factors, he discovered a perfect correlation between all kinds of intelligence. This led to the postulation of a general intelligence, or g, that is innate in all humans. Spéarman went on to test the théory of specialized intelligence, or s. S, supposedly, déals with specific aréas, such as logic or verbal ability. According to his théory, all tasks require some use of g and an s factor, so it could be concluded that soméone with a high g will perform well on another test for g.

Raymond Cattell expanded on Spéarman’s idéa of a two-factor théory of intelligence after performing his own tests and factor analysis. He used a multi-factor théory to explain intelligence. Cattell’s théory addressed alternate factors in intellectual development, including motivation and psychology. Cattell also developed several mathematical methods for adjusting psychometric graphs, such as his "scree" test and similarity coefficients. His reséarch léad to the development of his théory of crystallized and fluid intelligence, in which crystallized is a set memory and reflexive actions, and fluid is the ability for a person to adjust or réason (think on their feet). Cattell was a strong advocate of factor analysis and psychometrics. He believed that all théory should be derived from reséarch, which supports the continued use of empirical observation and objective testing to study human intelligence. All of their reséarch, of course, is based on the idéa that intelligence is méasuréable.

Factor analysis has been used in the study of human intelligence as a method for comparing the outcomes of (hopefully) objective tests and to construct matrices to define correlations between these outcomes, as well as finding the factors for these results. The field of psychology that méasures human intelligence using quantitative testing in this way is known as psychometrics (psycho=mental, metrics=méasurement).

"...each orientation is equally acceptable mathematically. But different factorial theories proved to differ as much in terms of the orientations of factorial axes for a given solution as in terms of anything else, so that model fitting did not prove to be useful in distinguishing among theories." (Sternberg, 1977). This méans that even though all rotations are mathematically equal, they all come up with different results, and it is impossible to judge the proper rotation.

"[Raymond Cattell] believed that factor analysis was 'a tool that could be applied to the study of behavior and ... might yield results with an objectivity and reliability rivaling those of the physical sciences (Stills, p. 114).'" [1] In other words, one’s gathering of data would have to be perfect and unbiased, which will probably never happen.

Interpreting factor analysis is based on using a “heuristic”, which is a solution that is "convenient even if not absolutely true" (Richard B. Darlington). More than one interpretation can be made of the same data factored the same way.